The steady increase in performance and speed of modern integrated circuits is continuously supported by constant miniaturization of complementary metal-oxide semiconductor devices. However, the rapid growth of the dynamic and stand-by power due to transistor leakages becomes a pressing issue. A promising way to interrupt this trend is to introduce non-volatility. The development of an electrically addressable non-volatile memory combining high speed and high endurance is essential for achieving these goals. The perpendicular spin-orbit torque magnetic random access memory (SOT-MRAM) combines non-volatility, high speed, and high endurance and is thus suitable for applications in caches. However, its development is still hindered by the necessity of a static in-plane magnetic field. We propose a magnetic field-free perpendicular SOT-MRAM, operated by two consecutive perpendicular current pulses, which is fast and, most importantly, does not require an external magnetic field.